"And our relationship with the United States is built on millions of Australians and Americans who have been working together, fighting together, serving together, for over a century."

Mr Turnbull went on to say the Australia and the US have a great deal in common.

"We have so much in common. Shared values,democracy, the rule of law, maintaining the international order upon which our security and prosperity depends," Mr Turnbull said.

"So the American people have made a great and momentous choice today. We congratulate president-elect Trump and we look forward to working closely as ever with his administration as it is formed and when it takes office earlier next year."

Opposition leader Bill Shorten took to Twitter to congratulate the new President.

"Australians should also know our alliance with the United States has grown and thrived for seven decades - no matter who's in charge, Mr Shorten wrote.

"It is far bigger than any individual, far more powerful than any personality - and it will endure."

However the Labor leader added statements indicating he wouldn't back down from the strident criticism he had directed towards the Republican leader during the campaign.

"If I see women being disrespected, I'm going to call it out," he wrote.

"If I see people being discriminated against because of the colour of their skin or their religion, I'm going to call it out."